He is banned from travelling can he delegate someone to do Hajj on his behalf?

So long as your brother hopes that he will be allowed to travel, and he will be able to do Hajj himself, then he does not have the option of delegating someone else to do Hajj on his behalf; rather he should be patient and wait, because delegating someone else to do it is only allowed for the one who is unable to do it and has no hope that the cause of his being unable will cease to apply. 

If it is decreed that he die before that, there will be no sin on him because he is excused. In that case, Hajj should be performed on his behalf with the expanses paid from his estate, or someone may voluntarily do Hajj on his behalf. 

Ibn Qudaamah (may Allaah have mercy on him) said: To sum up: if a person meets the conditions of Hajj being obligatory, but he is unable to do it for some reason that he has no hope will cease to apply, such as chronic sickness, or sickness for which there is no hope of recovery, or he is physically weak and is not able to sit firmly on his mount except with unbearable difficulty, or he is elderly, if there is someone who can do Hajj on his behalf and he can afford to send him on his behalf, then he must do that. This is the view of Abu Haneefah and al-Shaafa’i. … If a person has hope that he will recover from sickness or that his detainment will end, etc, then he does not have the right to delegate someone else, and if he does that, it is not valid. This is the view of al-Shaafa’i. That is because there is the hope that he will be able to do Hajj himself, so he does not have the right to delegate someone else, and it will not be valid if he does that. This is different from the one who has no hope of recovery, because he is totally unable and has no hope of being able to do it at all, and because the text speaks of doing Hajj on behalf of an elderly man, who is one who has no hope of being able to do Hajj for himself. No analogy can be made with that except in the case of one who is like him. End quote from al-Mughni (3/91). 

Your brother comes under the same ruling as one who is detained or imprisoned, as mentioned by Ibn Qudaamah (may Allaah have mercy on him). 

And Allaah knows best.